The Blazers' 140-137 victory took four overtimes to decide, BBC Sport reported.
The lead changed hands 24 times through the match before Seth Curry scored the deciding points with 2.8 seconds left.
"I have never been involved in a game like that in regular season or playoffs," said Blazers coach Terry Stotts.
"It was an amazing effort by both teams."
CJ McCollum scored 41 points for the Blazers in what was only the second quadruple-overtime playoff game in NBA history, making it the joint-longest playoff game of all time.
The Boston Celtics and the Syracuse Nationals also went to a fourth overtime in March 1953.
Rodney Hood's three-pointer gave Portland a 138-136 lead with 17.8 seconds left and Nikola Jokic had a chance to tie the game but missed one of two free throws before Curry sealed the win for the home side.
"That was the craziest game I have ever been a part of," said Damian Lillard, who scored 28 points for Portland.
"We fought, we fought, we fought. That's all you can ask for. It was a hell of basketball game by two very good basketball teams," added Denver coach Mike Malone.
The longest game in NBA history was a regular-season match when the Indianapolis Olympians and the Rochester Royals went to a sixth overtime – 78 minutes – in January 1951.
Elsewhere, the Milwaukee Bucks' 123-116 victory in Boston put them 2-1 up in their Eastern Conference playoff series against the Celtics.